Lecture in Philosophy and History of Science ( The 3rd CAPE Lectures) : Algorithmic interpretation of probability

Philosophy of probability is one of the big problem in science
discussed so far.
In this talk I first review the history of philosophy of probability.
Then I introduce theory of algorithmic randomness and its
related topic, which is produced by the study of the mathematical
formalization of probability.
Finally I discuss the notion of probability from the algorithmic
point of view by seeing the results that has got recently.

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction. In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics).

Sponsored by: Department of Philosophy and History of Science, Kyoto University